Please bare with me on what may seem like stupid questions, as I have yet to begin my Full Time RVing journey, so I know very little about this.

I'd like to know exactly how much trouble I can get into by parking my Casita TT at a beach or just any park? I understand I run the risk of hearing a knock at my door asking me to leave. Aside from that, do I get a ticket of some sort or do they usually just ask you to leave?

Just get a reservation if you drop the TT. We sometimes take long trips and do not have reservations. When DW gets tired she decides we're going to stop for awhile and I've always been able to find a campground with a site free. Happy travels.

you can overnight at many places: walmart, picnic rest stops (in Texas) interstate rest stops, home depots, flying j truck stops, cabelas, county fair grounds.
but I don't think it would be wise to unhook and leave the trailer alone at these places.

Overnight stops sometimes need to be carefully planned. Usually there is some place almost everywhere someone can pull over for a quick overnight sleep. There are many public places like city parks and beaches that do allow overnight stops, some free and some with a fee. There will usually be a sign to tell you what is doable. Some city ordinances do not allow parking on public streets even for quick overnight stops &/or long term. The same can be true in private parking lots like Wal*Mart, other retail stores or churches. Parking can & should be done by permission only if no city ordinance is violated.

There are resources for finding free or low cost boondocking sites but I can't direct to them. However, someone at this forum certainly may have that info.

No, you cannot just park wherever you are for the night. Many jurisdictions have laws against overnight camping in their public facilities as well as in store parking lots and even on the streets. Additionally, many places that are easily accessible with even a small trailer are not particularly safe at night. There are many low cost or even free campsites, and a previous poster listed some links. Passport America, a camping club that gives 50% discount on camp fees is another resource. Harvest Hosts is a club that gives free camping at wineries and farms.

It depends on the beach or park.. Some allow overnight, some do not, if it's posted "NO overnight parking" then a fine is the first level of discomfort. Tow and Impound is the 2nd, and of course not many towers know the proper way to hook up a motor home so damage is likely.

Home is where I park it.
Kenwood TS-2000 housed in a 2005 Damon Intruder 377

@OP, it all depends on the locality. Some places, nobody cares. Other places, the authorities will be all over you like a cheap suit. And as others have said, please do not attempt it without finding out first which it is where you are. Annoying the locals helps nobody.

Some states object mightily to transients sleeping over (even in an RV) in Interstate rest areas. Some take the more sensible approach that they'd prefer you not drive when exhausted, so sleep away. It is incumbent on YOU to know which it is. Usually there are signs saying "no overnight" but the mere absence of such signs should not be taken as an open invitation.

My daughter and son-in-law live in LA, and she tells me they have such a problem with otherwise homeless people living in RVs that there are city ordinances against it. She has told me that if we visit her in the RV, she can get a night-by-night permit to park the RV in front of their place, but not to attempt it without giving her enough notice to secure said permit.

On the other side of the coin, I've passed through Interstate rest areas that even had dump stations and special areas for RVs (but allow one-night only, it should be noted -- no hookups, they didn't want to make it TOO comfortable).